Difference between revisions of "Exponential Properties"

From Department of Mathematics at UTSA
Jump to navigation Jump to search
Line 7: Line 7:
 
* For any nonzero number <math> a </math>, <math> a^0 = 1 </math>.
 
* For any nonzero number <math> a </math>, <math> a^0 = 1 </math>.
 
* For any positive number <math> m </math>, <math> 0^m = 0 </math>.
 
* For any positive number <math> m </math>, <math> 0^m = 0 </math>.
* <math> 0^m </math> does not exist when m is negative (since <math> 0^{-n} = 1/0^n = 1/0 </math>), <math> 0^n </math> and is either undefined or indeterminate when <math> n = 0 </math> (that is, <math> 0^0 </math> is undefined or indeterminate depending on the context).
+
* <math> 0^m </math> does not exist when m is negative (since <math> 0^{-n} = 1/0^n = 1/0 </math>), and <math> 0^m </math> is either undefined or indeterminate when <math> m = 0 </math> (that is, <math> 0^0 </math> is undefined or indeterminate depending on the context).
  
 
==Resources==
 
==Resources==
 
* [https://tutoring.asu.edu/sites/default/files/exponentialandlogrithmicproperties.pdf Exponential and Logarithmic Properties], Arizona State University
 
* [https://tutoring.asu.edu/sites/default/files/exponentialandlogrithmicproperties.pdf Exponential and Logarithmic Properties], Arizona State University

Revision as of 13:05, 16 September 2021

Introduction

Exponential properties can be used to manipulate equations involving exponential expressions and/or functions. Here are some important exponential properties:

  • Negative exponent property: For any number , and .
  • Product of like bases: For

Special exponential properties involving 0:

  • For any nonzero number , .
  • For any positive number , .
  • does not exist when m is negative (since ), and is either undefined or indeterminate when (that is, is undefined or indeterminate depending on the context).

Resources